Hirzebruch and van der Geer attached theta functions to self-orthogonal,
$C\subseteq C^{\bot}$, linear codes $C\subseteq\mathbb F_p^n$, for $p$
an odd prime, and related them to the Lee weight enumerator for the code [5, Ch. 5].
Choie and Jeong extended this result to Jacobi theta functions and provided
an analytic proof of the Lee weight MacWilliams Identity for such $C$ [3].
We provide an analytic proof of the Hamming weight MacWilliams Identity
for linear codes $C\subseteq\mathbb F_p^n$, generalizing the seminal
result for binary codes $C\subseteq\mathbb F_2^n$ [2].